The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  0  1  1  1  1  1  0  1  1  1  1  1  1  1  3  1
 0  3  0  0  0 18  9 21  3 24  6 24 24 24 15 24  3 15 18  9 21  3 18  3  3 15 18 21 12 18  0  0 15 15 15 24 18 24  6
 0  0  3  0  9 21 21 15 12 12 15  3 15 18 24  3  3  0 24 15  6 18  0  9 12  9  6 15 21  9  6  0 21  0  6  9 12  6  0
 0  0  0  3 15 15 21  6 18  9 15 12 12  0 18 24  6  3  3  6  9 12  3  9 12 24 18 12 24  3 12 21 15  9 15  0  3  6  3

generates a code of length 39 over Z27 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+144x^69+156x^70+300x^71+578x^72+450x^73+624x^74+924x^75+1824x^76+1836x^77+5168x^78+3186x^79+1632x^80+1122x^81+408x^82+240x^83+360x^84+210x^85+180x^86+146x^87+78x^88+48x^89+60x^90+6x^91+2x^105

The gray image is a code over GF(3) with n=351, k=9 and d=207.
This code was found by Heurico 1.16 in 1.07 seconds.